Multivariate Distributions and Copulas

Abstract

Before we describe multivariate distribution, we review some notation and characteristics of univariate distributions. In general, we use capital letters for random variables and small letters for observed values, i.e., we write $X=x$. Here, we only consider absolutely continuous or discrete distributions, and therefore corresponding (conditional) densities or probability mass functions exist. In both cases, we use the letter f for densities or probability mass functions and the letter F for the corresponding distribution function.